White is NEVER ground. In this case, if it was on a switch it was being used as a hot.

I have no idea what you mean by "crossover". Do you mean jumper wires? If so numbers 1,2 & 3 mean nothing. We'd have to see a pic of the box and the new switch to eve begin to try and help.
Also, you'll need a real electrical tester, or DMM, and know how to use it to figure this out.

Yes, that makes sense. The white is the common and should go to the single screw. The 3 blacks to the 3 screws on the other side. Do I need to run a ground wire from the green ground screw to the electrical box or is it likely grounded at the light/exhaust fan/heat fan unit?

Here's pics of the old switch.

Thanks very much. You've already helped a great deal.

Forgot to add, yes, there are jumper wires on the old switch from 1 switch to the other going down. On the picture, the white is not where it original was, I just put it back in (CB is off) until I figured the new switch wiring out (with your help, much appreciated).

I connected white to the common screw and the 3 blacks to the other side.

The top switch now light correctly operates the light but the 2 fans only operate when the top switch light is ON. Does that mean the black wire currently connected to the light switch screw is actually the common and the white wire is actually the light wire?

What is the white stuff all over the switch? Is your picture of the old switch or the new one? The only thing I can say for certain is that the green screw on the switch definitely needs to be connected to a ground wire.